A box contains $n$ number of coins, $m$ of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is $1/2$, while it is $2/3$ when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows a head and the second time it shows tail. What is the probability that the coin drawn is fair.

3 Answers
3

What have you done so far? Hint: Without the flips, what is the chance you draw a fair coin? If you draw a fair coin, what is the chance you get the flips specified? If you draw a biased coin, what is the chance?

I know this isn't really answering your question, but a coin toss, is rarely ever fair. And I'm not talking a few thousandths of a percent, but more like 52% vs 48%. Below makes for fascinating reading: